Difference between revisions of "ApCoCoA-1:Bertini.BZCSolve"
From ApCoCoAWiki
| Line 8: | Line 8: | ||
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||
| + | |||
| + | This function uses total degree homotopy to find all isolated solutions of a zero dimensional system of polynomial equaions. It enables you to use all kinds of user configurations provided by Bertini. Please read about configuration settings provided in Bertini manual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt></item>. The system of polynomials may be homogeneous or nonhomogeneous. For homogeneous polynomial system the output will be the list of all real solutions and for nonhomogeneous system the output will be the list of all finite solutions | ||
<itemize> | <itemize> | ||
<item>@param <em>P</em>: List of polynomials of the given system.</item> | <item>@param <em>P</em>: List of polynomials of the given system.</item> | ||
| Line 32: | Line 34: | ||
-- And we achieve a list of lists containing all finite solutions. | -- And we achieve a list of lists containing all finite solutions. | ||
---------------------------------------- | ---------------------------------------- | ||
| − | [[Vector(500000000000000870080079571456753631209/500000000000000000000000000000000000000, | + | [ |
| + | [ | ||
| + | Vector(500000000000000870080079571456753631209/500000000000000000000000000000000000000, | ||
41243336046164965623860294533917 3594181/200000000000000000000000000000000000000000000000000000), | 41243336046164965623860294533917 3594181/200000000000000000000000000000000000000000000000000000), | ||
Vector(199999999999999920289038441185562687901/100000000000000000000000000000000000000, | Vector(199999999999999920289038441185562687901/100000000000000000000000000000000000000, | ||
| − | -4918613303067726249865351347506841944303/5000000000000000000000000000000000000000000000000000000)], | + | -4918613303067726249865351347506841944303/5000000000000000000000000000000000000000000000000000000) |
| − | + | ], | |
| + | [ | ||
| + | Vector(999999999999996907691691548150283767063/500000000000000000000000000000000000000, | ||
4026821783991733021565024336088959292491/1000000000000000000000000000000000000000000000000000000), | 4026821783991733021565024336088959292491/1000000000000000000000000000000000000000000000000000000), | ||
Vector(1000000000000008119524837615406734621127/1000000000000000000000000000000000000000, | Vector(1000000000000008119524837615406734621127/1000000000000000000000000000000000000000, | ||
| − | -9202828375000265851232972557923998357683/1000000000000000000000000000000000000000000000000000000)], | + | -9202828375000265851232972557923998357683/1000000000000000000000000000000000000000000000000000000) |
| − | + | ], | |
| + | [ | ||
| + | Vector(-1999999999999981470621955122058645854307/1000000000000000000000000000000000000000, | ||
-2219296880596437220953595963738223862847/100000000000000000000000000000000000000000000000000000), | -2219296880596437220953595963738223862847/100000000000000000000000000000000000000000000000000000), | ||
Vector(-1000000000000016429280952166817619195409/1000000000000000000000000000000000000000, | Vector(-1000000000000016429280952166817619195409/1000000000000000000000000000000000000000, | ||
| − | 2246895233251384601549113345810086172711/100000000000000000000000000000000000000000000000000000)], | + | 2246895233251384601549113345810086172711/100000000000000000000000000000000000000000000000000000) |
| − | + | ], | |
| + | [ | ||
| + | Vector(-9999999999999986714415752390569533003343/10000000000000000000000000000000000000000, | ||
2376331150450927561422763997224327498341/1000000000000000000000000000000000000000000000000000000), | 2376331150450927561422763997224327498341/1000000000000000000000000000000000000000000000000000000), | ||
Vector(-200000000000000126515279556718539177417/100000000000000000000000000000000000000, | Vector(-200000000000000126515279556718539177417/100000000000000000000000000000000000000, | ||
| − | -409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000)]] | + | -409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000) |
| + | ] | ||
| + | ] | ||
--The elements of lists are vectors. Each vector represents a complex number. For example Vector(5000/1000,-4150/1000) | --The elements of lists are vectors. Each vector represents a complex number. For example Vector(5000/1000,-4150/1000) | ||
| Line 69: | Line 81: | ||
-- And we achieve a list of lists containing all real solutions. | -- And we achieve a list of lists containing all real solutions. | ||
---------------------------------------- | ---------------------------------------- | ||
| − | [[-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, | + | [ |
| + | [-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, | ||
-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, | -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, | ||
| − | -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000], | + | -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000 |
| − | + | ], | |
| + | [ | ||
| + | -666269356331265789905402745641735631587/1250000000000000000000000000000000000000, | ||
-666269356331265789905402745641735631587/1250000000000000000000000000000000000000, | -666269356331265789905402745641735631587/1250000000000000000000000000000000000000, | ||
| − | 666269356331265789905402745641735631587/1250000000000000000000000000000000000000], | + | 666269356331265789905402745641735631587/1250000000000000000000000000000000000000 |
| − | + | ], | |
| + | [ | ||
| + | -1961395985465574251430275441821775811231/20000000000000000000000000000000000000000000000000000, | ||
1604689603443950100804972123829819895459/2500000000000000000000000000000000000000, | 1604689603443950100804972123829819895459/2500000000000000000000000000000000000000, | ||
| − | -9839275092234527567507618459170114455473/100000000000000000000000000000000000000000000000000000], | + | -9839275092234527567507618459170114455473/100000000000000000000000000000000000000000000000000000 |
| − | + | ], | |
| + | [ | ||
| + | -1197970328164235882805480928545099670003/10000000000000000000000000000000000000000000000000000, | ||
3209379206887735502321156763919697536571/5000000000000000000000000000000000000000, | 3209379206887735502321156763919697536571/5000000000000000000000000000000000000000, | ||
| − | -4210800092649494941547012623104854361/31250000000000000000000000000000000000000000000000]] | + | -4210800092649494941547012623104854361/31250000000000000000000000000000000000000000000000 |
| + | ] | ||
| + | ] | ||
--For Bertini output files please refer to ApCoCoA directory/Bertini. | --For Bertini output files please refer to ApCoCoA directory/Bertini. | ||
Revision as of 09:51, 13 May 2010
Bertini.BZCSolve
Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations using configurations provided by the user.
Syntax
Bertini.BZCSolve(P:LIST, SysTyp:STRING , ConfigSet:LIST):LIST
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
This function uses total degree homotopy to find all isolated solutions of a zero dimensional system of polynomial equaions. It enables you to use all kinds of user configurations provided by Bertini. Please read about configuration settings provided in Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</item>. The system of polynomials may be homogeneous or nonhomogeneous. For homogeneous polynomial system the output will be the list of all real solutions and for nonhomogeneous system the output will be the list of all finite solutions
@param P: List of polynomials of the given system.
@param SysTyp: Type of polynomials in the List P. Homogeneous ("hom") or non-homogeneous ("Nhom").
@param ConfigSet: List of strings representing configurations to be used. Bertini uses multiple configuration settings. These configurations should be provided by the user. If you want to use default configurations then leave this list empty. For details about configuration settings see Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf
@return A list of lists containing the finite (or real) solutions of the polynomial system P.
.
Example
-- An example of zero dimensional Non-homogenous solving with fixed higher precision. -- We want to solve the zero dimensional non-homogenous system x^2+y^2-5=0, xy-2=0, for fixed higher precision. Use S ::= QQ[x,y]; P := [x^2+y^2-5,xy-2]; SysTyp := <quotes>Nhom</quotes>; ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>]; -- Then we compute the solution with Bertini.BZCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing all finite solutions. ---------------------------------------- [ [ Vector(500000000000000870080079571456753631209/500000000000000000000000000000000000000, 41243336046164965623860294533917 3594181/200000000000000000000000000000000000000000000000000000), Vector(199999999999999920289038441185562687901/100000000000000000000000000000000000000, -4918613303067726249865351347506841944303/5000000000000000000000000000000000000000000000000000000) ], [ Vector(999999999999996907691691548150283767063/500000000000000000000000000000000000000, 4026821783991733021565024336088959292491/1000000000000000000000000000000000000000000000000000000), Vector(1000000000000008119524837615406734621127/1000000000000000000000000000000000000000, -9202828375000265851232972557923998357683/1000000000000000000000000000000000000000000000000000000) ], [ Vector(-1999999999999981470621955122058645854307/1000000000000000000000000000000000000000, -2219296880596437220953595963738223862847/100000000000000000000000000000000000000000000000000000), Vector(-1000000000000016429280952166817619195409/1000000000000000000000000000000000000000, 2246895233251384601549113345810086172711/100000000000000000000000000000000000000000000000000000) ], [ Vector(-9999999999999986714415752390569533003343/10000000000000000000000000000000000000000, 2376331150450927561422763997224327498341/1000000000000000000000000000000000000000000000000000000), Vector(-200000000000000126515279556718539177417/100000000000000000000000000000000000000, -409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000) ] ] --The elements of lists are vectors. Each vector represents a complex number. For example Vector(5000/1000,-4150/1000) --represents the complex number 5000/1000-4150/1000i. --For Bertini output files please refer to ApCoCoA directory/Bertini.
Example
-- An example of zero dimensional homogenous solving with fixed higher precision -- We want to solve the zero dimensional homogenous system x^2-z^2=0, xy-z^2=0, for fixed higher precision. Use S ::= QQ[x,y]; P := [x^2-z^2, xy-z^2]; SysTyp := <quotes>hom</quotes>; ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>]; -- Then we compute the solution with Bertini.BZCSolve(P,SysTyp,ConfigSet); -- And we achieve a list of lists containing all real solutions. ---------------------------------------- [ [-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000 ], [ -666269356331265789905402745641735631587/1250000000000000000000000000000000000000, -666269356331265789905402745641735631587/1250000000000000000000000000000000000000, 666269356331265789905402745641735631587/1250000000000000000000000000000000000000 ], [ -1961395985465574251430275441821775811231/20000000000000000000000000000000000000000000000000000, 1604689603443950100804972123829819895459/2500000000000000000000000000000000000000, -9839275092234527567507618459170114455473/100000000000000000000000000000000000000000000000000000 ], [ -1197970328164235882805480928545099670003/10000000000000000000000000000000000000000000000000000, 3209379206887735502321156763919697536571/5000000000000000000000000000000000000000, -4210800092649494941547012623104854361/31250000000000000000000000000000000000000000000000 ] ] --For Bertini output files please refer to ApCoCoA directory/Bertini.
See also
